Specific heat measuring method and instrument

ABSTRACT

In order to measure specific heat, the measurement time is very long and the instrument is very expensive. The specific heat may be calculated based on the thermal time constant obtained from the change of the sample temperature when the predetermined amount of sample with known density at the first temperature is introduced in the environment at the second temperature. This measuring method can use the oscillatory densitometer. The predetermined amount corresponds to the volume of the sample to be introduced in the oscillatory densitometer, the density is a measurement result of the oscillatory densitometer, and the thermal time constant corresponds to the time constant of the oscillation period of the oscillatory densitometer.

FIELD OF THE INVENTION

This invention relates to a method of measuring specific heat and aninstrument thereof, and more specifically relates to a specific heatmeasuring method and instrument using thermal time constant.

DESCRIPTION OF THE RELATED ART

The measurement of specific heat has been performed by a large-scaleinstrument. For instance, in a differential scanning calorimeter, areference material r and a sample s are placed in holders 42 r and 42 sin an electric furnace 40, and a program temperature control means 45heats the electric furnace so that the rate of the temperatureincreasing is kept at a constant, as shown in FIG. 8. The temperaturedifference between the sample s and the reference material r is detectedby a temperature difference detecting means 43. In order to keep thetemperature difference “0” a differential power compensation circuit 44controls heaters 41 r and 41 s to heat the electric furnace.

Under such configuration, the specific heat of the sample s is found inconsideration of heat flow rates of the sample s and the referencematerial r in the holders 42 s and 42 r (“Foundation of Thermal Analysisfor Materials Science” written by Yasutoshi Saitoh, Kyoritsu PublishingCo., Ltd., Oct. 5, 1996).

SUMMARY OF THE INVENTION

However, there are disadvantages in the above-mentioned instrument; theconfiguration gets large scale; it takes a very long time to find thespecific heat for one sample; and, both the instrument cost and thepersonal expense become expensive.

The invention is suggested in view of the above-mentioned problems, andit has an object to provide a specific heat instrument of which cost isvery low and that requires a very short measurement time.

The present invention is characterized that a predetermined amount ofsample with known density at a first temperature is introduced to anenvironment of a second temperature, a thermal time constant is obtainedfrom a change of the sample temperature with time in the environment ofthe second temperature, and a specific heat is calculated by theobtained thermal time constant.

The specific heat can be calculated by means of an oscillatorydensitometer. That is to say, the predetermined amount of samplecorresponds to an amount of sample to be introduced in a capillary tube(measurement cell) of the oscillatory densitometer, and the change ofthe sample temperature corresponds to the change of the oscillationperiod of the capillary tube. The density is a measurement result of theoscillatory densitometer, and the thermal time constant is allowed tocorrespond to a time constant of the oscillation period of the capillarytube of the oscillatory densitometer. The time constant can be found inprocess of calculating the density by a calculating unit.

In another aspect of the present invention, it may be configured tocalculate the specific heat of the sample based on the response of thesample temperature detected as follows. The response of the sampletemperature with change of the environment temperature is detected, whenthe predetermined amount of sample with known density is placed in anenvironment at the first temperature.

In this case, the measurement cell corresponds to the capillary tube ofthe oscillatory densitometer holding the sample of the predeterminedamount, and the density is the result calculated by the calculating unitof the oscillatory densitometer. A temperature measuring unitcorresponds to the period detecting unit of the oscillatorydensitometer, the sample temperature corresponds to an oscillationperiod of the capillary tube, and the calculating unit corresponds to acalculating unit of the oscillatory densitometer, and the change of thesample temperature corresponds to a phase change of the oscillationperiod.

The present invention makes it possible to measure the specific heat ofsample in a very simple manner. Since the specific heat can be measuredby a very simple configuration of instrument, it is possible to reducethe instrument cost extremely. In addition, the oscillatory densitometercan measure the specific heat and the density simultaneously.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagram explaining a principle of the invention.

FIG. 2 is a graph of time constant vs. density × specific heat.

FIG. 3 is a graph of actual measured value of specific heat vs. specificheat.

FIG. 4 is a conceptual diagram of oscillatory densitometer.

FIG. 5 is a block diagram showing circuits of the oscillatorydensitometer.

FIG. 6 is a diagram showing a phase difference between an environmenttemperature and a sample temperature.

FIG. 7 is a diagram showing a phase difference between an environmenttemperature and a sample temperature.

FIG. 8 is a diagram of prior art.

DETAILED DESCRIPTION OF THE INVENTION

FIG. 1 is a diagram explaining a principle of the invention.

A predetermined amount of sample at a first temperature t₁ is introducedin a measurement cell 1 of a measurement chamber 10, of whichtemperature is controlled to a second temperature t₀ being differentfrom the first temperature t₁, and a change of the sample temperature ismeasured by a temperature measuring unit 2. With the assumption that atemperature control unit 4 keeps the temperature of the measurementchamber 10 at the above temperature t₀, the temperature of the samplestarts to vary (increase or decrease) to an endpoint temperature that isthe second temperature t₀, depending on the time constant. A calculatingunit 3 calculates the time constant based on the change of the sampletemperature obtained by the temperature measurement unit 2, and itsresult depends on a material of the sample.

As a matter of course, it can be assumed that, in case of the samedensity of materials, the larger the specific heat is, the slower thedegree of the temperature gradient gets. And in case of the samespecific heat of the materials, the larger the density is, the slowerthe degree of the temperature gradient gets. It is not difficult tounderstand that the time constant is concerned with the specific heatand the density.

Therefore, in case of the material (gas and liquid) of which specificheat and density are known, a graph in which the specific heat x thedensity is set to a horizontal axis and the time constant at thetemperature increase (decrease) is set to the vertical axis shows astraight line as shown in FIG. 2. At this time, the change of the sampletemperature is measured after the sample at the temperature t₁ isintroduced into the environment at temperature t₀, and the time constantis found from the detected change of the sample temperature with time.However, the time constant can be found from the change of anoscillation period of the oscillatory densitometer as described below.

If an equation to express the straight line shown in FIG. 2 is known,the specific heat can be calculated by finding values of the thermaltime constant and the density. Where x_(H2O) represents the specificheat of water, d_(H2O) represents the density of water, x_(air)represents the specific heat of air, and d_(air) represents the densityof air, the straight line shown in FIG. 2 is given by an equation (1).

$\begin{matrix}\left( {{Equation}\mspace{14mu} 1} \right) & \; \\{\tau = {{\frac{\tau_{H2O} - \tau_{air}}{{x_{H2O}d_{H2O}} - {x_{air}d_{air}}}{xd}} + \tau_{0}}} & (1)\end{matrix}$

As the specific heat x and the density d of air and water respectivelyare shown in table 1, the equation (1) is defined to equations (2) and(3).

TABLE 1 Sample Specific heat × (JK⁻¹g⁻¹) Time constant τ (sec) Air1.0165 (300 K) 8.12 Water 4.1782 (30° C.) 37.25(Equation 2)τ=7.00422xd+8.11173  (2)

In result, an equation (3) to find the specific heat is obtained by thetime constant τand the density d that are obtained by the measurement.

$\begin{matrix}\left( {{Equation}\mspace{14mu} 3} \right) & \; \\{x = \frac{\tau - 8.11173}{7.00422d}} & (3)\end{matrix}$

Using an actual measured density d and a detected time constant τ to theabove equation (3), each specific heat of various liquids can becalculated. The calculated results are shown in a left column of Table 2as “actual measured value x” while the specific heats defined by thetechnical literature are shown in a right column of Table 2. A graph,representing the specific heat defined by the technical literatures andthe calculated specific heats, is shown in FIG. 3. It is obvious thatthe specific heat found by the method in the present inventioncorresponds to the specific heat in the technical literature.

TABLE 2 Calculation Result of Specific Heat Actual Specific TimeMeasured heat Density d constant Value × Sample Name (JK⁻¹g⁻¹) (gcm⁻³)^(τ)(sec) (Jg⁻¹K⁻¹) Air 1.02 0.00116 8.12 1.016 Methanol 2.53 0.7818222.18 2.569 Ethanol 2.44 0.78083 21.92 2.525 Hexane 2.17 0.65155 18.862.355 Acetone 2.26 0.78533 20.18 2.194 Degassed pure water 4.18 0.9956737.25 4.178 Ethylene glycol 2.39 1.10627 27.10 2.451 Aniline 2.061.01309 23.04 2.104 Glycerin 2.38 1.25558 29.65 2.449 Glycerin Solution3.42 1.11540 34.74 3.408

Japanese Patent No. 2,061,924, of which applicant is the same thisinvention, discloses a oscillatory densitometer as shown in FIG. 4 andFIG. 5 that is configured as follows.

It is configured that a U-shaped capillary tube 1 forming themeasurement cell is provided to the measurement chamber 10 to allow apredetermined amount of liquid or gas sample to be introduced in theU-shaped capillary tube.

When a drive pulse current S2 is provided from a pulse generator 13 to adriving coil 31, an external force is given to the capillary tube 1through a magnetic material 4 equipped at a tip of the capillary tube 1,and the capillary tube 1 starts to oscillate. A period detecting unit 15processes a sine wave S₂ generating at a detecting coil 21 in responseto the oscillation, and finds an oscillation period of the capillarytube 1. According to the result, a calculation unit 16 finds the densityof the sample. Besides, the drive current S₁ is given at a predeterminedtime interval synchronizing with the detected sine wave S₂.

A driving unit 3 (the driving coil 31 and the magnetic material 4) givesthe driving force to the capillary tube 1, while keeping the temperatureof the measurement chamber 10 at a predetermined temperature t₀ (thesecond temperature), (as a mater of course, the sample temperature isalso kept at the second temperature t₀). According to the naturaloscillation period T₀ at this time, the density d can be found byfollowing equation (4).

$\begin{matrix}\left( {{Equation}\mspace{14mu} 4} \right) & \; \\{d_{x} = {d_{A} - {\frac{T_{A}^{2} - T_{x}^{2}}{T_{A}^{2} - T_{B}^{2}}\left( {d_{A} - d_{B}} \right)}}} & (4)\end{matrix}$

d_(x): density of sample

d_(A): density of reference material A

d_(B): density of reference material B

T_(x): oscillation period of sample

T_(A): oscillation period of sample A

T_(B): oscillation period of sample B

When the sample at the first temperature t₁ is introduced in themeasurement chamber 10 of which temperature is kept at the othertemperature t₀, the sample temperature varies from the first temperaturet₁ to the second temperature t₀ according to a predetermined constant.At this time, the oscillation period also varies together with thechange of temperature, and it is sure that the change of oscillationperiod depends on the predetermined time constant.

Therefore, the time constant that defines the change of the temperaturefrom the first temperature t₁ to the second temperature t₀ can be foundby measuring the change of the oscillation period of the capillary tube1.

The oscillation period at the second temperature t₀ cannot be found onlyat the second temperature t₀. By measuring the change of the oscillationperiod (the change of temperature) after the sample at the firsttemperature t₁ is introduced in the capillary tube 1, the oscillationperiod can be calculated even not at the second temperature t₀. Thecalculation method thereof is disclosed in details in Japanese PatentNo. 2,061,924 (Japanese Patent Publication No. 07-104249 A) which waspatented by the applicant.

That is to say, the temperature t of the sample introduced in themeasurement chamber 1 varies depending on a time s, as defined inequation (5).

$\begin{matrix}\left( {{Equation}\mspace{14mu} 5} \right) & \; \\{t = {t_{0}\left( {1 - {{\mathbb{e}}\frac{t_{x} - s}{\tau_{x}}}} \right)}} & (5)\end{matrix}$

t₀: convergence temperature

τ_(x): time constant depending on sample

t_(x): constant depending on a first temperature of sample

From the change of temperature, it is possible to analogize that theperiod T varies as expressed in equation (6). The validity of theanalogical interpretation is based on the description in Japanese PatentPublication No. 07-104249A.

$\begin{matrix}\left( {{Equation}\mspace{14mu} 6} \right) & \; \\{T = {T_{0}\left( {1 - {{\mathbb{e}}\frac{t_{T} - s}{\tau_{T}}}} \right)}} & (6)\end{matrix}$

T₀: convergence period

τ_(t): time constant depending on sample

t_(T): constant depending on a first temperature of sample

By differentiating the both sides of the equation (6), followingequation is obtained.

$\begin{matrix}\left( {{Equation}\mspace{14mu} 7} \right) & \; \\{{T^{\prime} = {{\alpha\; T} + \beta}}{{where},{\alpha = {{{- \frac{1}{\tau_{T}}}\mspace{25mu}\beta} = {- \frac{T_{0}}{\tau_{T}}}}}}} & (7)\end{matrix}$

According to the above equation, the oscillation period detecting unit15 detects an oscillation period T at the time s after the sample isintroduced in the capillary tube 1, and the calculation unit 16determines α based on the oscillation period T and the differentiatedvalue using the least square method. From the αvalue, the time constantcan be determined.

Since the instrument is an oscillatory densitometer, it is able todetect the density at the same time. In addition, since the introducedvolume of the sample is fixed, it is possible to obtain all thenecessary data at the same time.

As described above, the specific heat can be found from the timeconstant corresponding to the change of the sample temperature under theenvironment, and the time constant can be found from a phase differencebetween the environment temperature and the sample temperature when theenvironment temperature varies periodically.

In other words, as shown in FIG. 6, when a very little periodical changeof temperature is given to a fixed environment temperature t₁₀, thesample temperature t₂₀ varies following to the environment temperaturet₁₀, and a phase difference θ is observed between the environmenttemperature t₁₀ and the sample temperature t₂₀.

The relation between the phase difference θand the time constant τbecomes θ=−tan⁻¹(ωτ). Based on this relation, the time constant τ can befound. In this case, as described in the aforementioned firstembodiment, if the sample temperature t₂₀ is not set to be differentfrom the environment temperature t₁₀ in advance, the time constant τ canbe found.

In addition, as shown in FIG. 7( a) and FIG. 7( b), as well as a verysmall periodical change of temperature is given to the environmenttemperature t₁₀, a center temperature t₃₀ varies continuously withslower pace more than the periodical change, it is possible tocontinuously measure the specific heat at each temperature.

In the above two cases, the oscillatory densitometer can be used. Thatis to say, the environment temperature t₁₀ can be obtained by varying acontrol temperature of the measurement chamber. Since the oscillationperiod T of the capillary tube depends on the sample temperature t₂₀ atthat time, the change of the sample temperature t₂₀ can be obtained byfinding the change of the oscillation period T. Therefore, the phasedifference between the environment temperature t₁₀ and the sampletemperature t₂₀ can be obtained from the change of the phase differenceof the oscillation period T of the capillary tube 1.

1. A specific heat measuring method comprising: introducing apredetermined amount of sample with known density at a first temperatureinto an environment at a second temperature; obtaining a thermal timeconstant from a change with time of sample temperature in theenvironment at the second temperature; and calculating a specific heatbased on the thermal time constant and on said density, wherein thepredetermined amount of sample corresponds to a volume of sample to beintroduced into an oscillatory densitometer, the density is ameasurement result of the oscillatory densitometer, and the thermal timeconstant corresponds to a time constant of oscillation period of theoscillatory densitometer.
 2. A specific heat measuring method accordingto claim 1, wherein said thermal time constant is linearly related to aproduct between said specific heat and said density.
 3. A specific heatmeasuring method comprising: placing a predetermined amount of samplewith known density into an environment at a first temperature; detectinga change of the sample temperature when the temperature of theenvironment varies; and calculating a specific heat of the sample basedon the change of the sample temperature in the environment and based onsaid density, wherein the specific volume corresponds to a volume ofsample to be introduced into an oscillatory densitometer, the density isa measurement result of the oscillatory densitometer, and the variationof sample temperature corresponds to the change of the oscillationperiod of the oscillatory densitometer depending on the change ofenvironment temperature.
 4. A specific heat measuring method accordingto claim 3, wherein said specific heat is calculated using a timeconstant that is determined from a phase difference between theenvironment temperature and the sample temperature when the environmenttemperature varies periodically.
 5. A specific heat measuring instrumentcomprising: a measurement cell holding a predetermined amount of samplewith a predetermined density; a measurement chamber provided with themeasurement cell therein and of which inside temperature is controlledat a predetermined temperature; a temperature measuring unit measuring achange of the sample temperature with time when the sample at a firsttemperature is introduced into the measurement cell controlled at asecond temperature; and a calculating unit calculating a specific heatbased on a thermal time constant of the sample obtained from the changeof the sample temperature with time and based on said density, whereinthe measurement cell corresponds to a capillary tube of an oscillatorydensitometer holding the predetermined amount of sample, the density isa result calculated by a calculating unit of the oscillatorydensitometer, the temperature measuring unit corresponds to a perioddetecting unit of the oscillatory densitometer, the sample temperaturecorresponds to a oscillation period of the capillary tube, thecalculating unit corresponds to a calculating unit of the oscillatorydensitometer, and the thermal time constant corresponds to a timeconstant of the oscillation period.
 6. A specific heat measurementinstrument according to claim 5, wherein said thermal time constant islinearly related to a product between said specific heat and saiddensity.
 7. A specific heat measurement instrument comprising: ameasurement cell holding a predetermined amount of sample with apredetermined density; a measurement chamber provided with themeasurement cell therein and of which inside temperature is controlled;a temperature measuring unit measuring a change of the sampletemperature with time when the sample is introduced into the measurementcell and the temperature of the measurement cell varies; and acalculating unit calculating a specific heat based on the change of thesample temperature with time when the temperature of the measurementcell varies and based on said density, wherein the measurement cellcorresponds to a capillary tube of an oscillatory densitometer holdingthe predetermined amount of sample, the density is a result calculatedby a calculating unit of the oscillatory densitometer, the temperaturemeasuring unit corresponds to a period detecting unit of the oscillatorydensitometer, the sample temperature corresponds to an oscillationperiod of the capillary tube, the calculating unit corresponds to acalculating unit of the oscillatory densitometer, and the change of thesample temperature with time corresponds to a phase change of theoscillation period.
 8. A specific heat measurement instrument accordingto claim 7, wherein said specific heat is calculated using a timeconstant that is determined from a phase difference between theenvironment temperature and the sample temperature when the measurementcell temperature varies periodically.
 9. A specific heat measuringmethod comprising: introducing a predetermined amount of sample withknown density at a first temperature into an environment at a secondtemperature; obtaining a thermal time constant from a change with timeof sample temperature in the environment at the second temperature; andcalculating a specific heat based on a linear relationship between thethermal time constant, and the density multiplied by the specific heat.